An Alternative Algorithm for Classification Based on Robust Mahalanobis Distance

Abstract

This study considers the classification problem for binary output attribute when input attributes are drawn from multivariate normal distribution, in both clean and contaminated case. Classical metrics are affected by the outliers, while robust metrics are computationally inefficient. In order to achieve robustness and computational efficiency at the same time, we propose a new robust distance metric for K-Nearest Neighbor (KNN) method. We call our proposed metric Alternative Robust Mahalanobis Distance (ARMD) metric. Thus KNN using ARMD is alternative KNN method. The classical metrics use non robust estimate (mean) as the building block. To construct the proposed ARMD metric, we replace non robust estimate (mean) by its robust counterpart median. Thus, we developed ARMD metric for alternative KNN classification technique. Our simulation studies show that the proposed alternative KNN method gives better results in case of contaminated data compared to the classical KNN. The performance of our method is similar to classical KNN using the existing robust metric. The major advantage of proposed method is that it requires less computing time compared to classical KNN that using existing robust metric.